Question

Hi I cricled the correct answer but I just need to solve how to get it.

Answer 1

In order to solve this problem we are gonna use a trick that consist in expressing 64 and 16 as powers of 2.

We can write 64 and 16 in the following way:

`\begin{gathered} 64=2^6 \\ 16=2^4 \end{gathered}`

Now, we replace the equations of above in the equation of the statement:

`\begin{gathered} (2^6)^(2x)=2^4 \\ 2^(6\cdot2x)=2^4 \\ 2^(12x)=2^4 \end{gathered}`

In the intermediate steps we have aplied the rule that the powers multiply.

Now, in the last equation, the exponents must be equal if want to have both sides of the equation equal. So:

`\begin{gathered} 12x=4 \\ x=(4)/(12)=(1)/(3) \end{gathered}`

The correct answer is B